'Use Multiple GDK Display Back-Ends Simultaneously (in Docker)?

I apologize in advance if the answer to this question is an obvious "no," but in the interest of leaving no stone unturned (and the fact that I am by no means an expert in this area), I am hazarding asking this question here:

I have a GTK application that I would like to have running on a web page. I have the application running in a Docker container and I am using the GDK Broadway HTML5 backend in order to run the application via a web browser using:

ENV GDK_BACKEND broadway
ENV BROADWAY_DISPLAY :5

The application runs great, save for one particular issue. I am embedding a python matplotlib process into a container from the GTK application using GtkSocket/Plug, which follows the XEmbed Protocol (X11). This is obviously a different display than Broadway and thus it does not work. I suspect that it is not possible, but just in case there is something clever that could be done (keeping in mind that the application is running in a Docker container), is there any way possible to essentially have more than one GDK back-end display server running simultaneously (here X11 and Broadway)?



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